Bloch-Siegert shift in an interacting Bose-Einstein condensate

The Bloch-Siegert shift $\cite{Bloch}$ (BSS) is a paradigmatic frequency shift that arises from the nonlinear response of a two-level system (TLS) subjected to strong driving fields. When a TLS is driven by a linearly polarized field, the co-rotating-wave component leads to the famous Rabi oscillations. By contrast the co-rotating-wave component, whose role is usually neglected in a weak driving, leads to a frequency shift of the TLS resonance frequency. This phenomenon is encountered in various areas, from quantum optics to nuclear magnetic resonance.\par Here, we investigate the BSS in a box-trapped ${}^{87}\!Rb$ Bose-Einstein condensate (BEC) driven by a strong oscillating magnetic field gradient $\cite{Nir}$. By tuning the chemical potential of the gas, we investigate how the BSS evolves from the ideal shift of the two lowest energy levels of a single particle in a box to the unexplored shift of long-wavelength collective excitations of the interacting BEC. \begin{thebibliography} \small \bibitem{Bloch} F. Bloch and A. Siegert, Phys. Rev. 57, 522 (1940). \bibitem{Nir} N. Navon, A. L. Gaunt, R. P. Smith and Z. Hadzibabic, Nature 539, 72 (2016). \end{thebibliography}